Electronic structure of conjugated oligomers that are building blocks for achiral and chiral graphene nanoribbons

The understanding of graphene x-electronic structure is further advanced by presenting the exact solution of the tight-binding eigenvalue problem for conjugated oligomers (polyparaphenylene (PPP) and polynaphthalene (PN) of different lengths), which can serve as building blocks for armchair and (2m, m) graphene nanoribbons. The problem is considered on the basis of the Su-Schrieffer-Heeger-Huckel-type Hamiltonian. We show that the x-electron spectrum of PN includes the local states unlike the spectrum of PPP consisting (as well as spectra of armchair graphene nanoribbons of arbitrary widths) only of extended states and present explicit analytic expressions for the wave functions of the conjugated oligomers.